‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

Support Vector Machine (SVM) is one of the most robust and accurate method amongst all the supervised machine learning techniques. Still, the performance of SVM is greatly influenced by the selection of kernel function. This research analyses the characteristics of the two well known existing kernel functions, local Gaussian Radial Basis Function and global Polynomial kernel function. Based on ...

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...

"Estimation of the value of a regression function at a point of continuity using a kernel-type estimator is discussed and improvements of the technique by a generalized jackknife estimator are presented. It is shown that the generalized jackknife technique produces estimators with faster bias rates. In a small example it is investigated, if the generalized jackknife method works for all choices...

p|n p is the well-known kernel function and P (n) is the largest prime factor of n. In particular, we show that the maximal order of γ2(n) for n ≤ x is (1 + o(1))x/ log x as x → ∞ and that ∑n≤x 1/γ2(n) = (1+ o(1))ηx/ log x, where η = ζ(2)ζ(3)/ζ(6). We further show that, given any positive real number u < 1, limx→∞ 1 x#{n ≤ x : γ2(n) < xu} = limx→∞ 1 x#{n ≤ x : n/P (n) < xu} = 1− ρ(1/(1− u)), wh...

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

The use of different kernel functions in SVM (Support Vector machines) has been reported in the literature. In this paper, the use of the q-Gaussian function as kernel function in SVM is investigated and q-Gaussian function is explored. While the q-Gaussian kernel SVM classifiers being built, cross validation methods are used to select the non-extensive entropic index q under varying feature si...

Small Area estimation is a technique used to estimate parameters of subpopulations with small sample sizes.  Small area estimation is needed  in obtaining information on a small area, such as sub-district or village.  Generally, in some cases, small area estimation uses parametric modeling.  But in fact, a lot of models have no linear relationship between the small area average and the covariat...